The classical foundations of deterministic theoretical population genetics are Wright's "mean fitness principle" and Fisher's "fundamental theorem," which govern the dynamics of one-locus viability selection models. The P.I. has developed an analytical method for generating Lyapunov functions for a more general class of models incorporating frequency dependent selection. Specifically, general dynamic rules have been derived for models with selection in both prezygotic and zygotic stages, and for models in which fitness is a polynomial function of allelic frequency of arbitrary positive degree. Further development and application of the analytic method will concentrate on four types of models of general interest to evolutionary biologists: (1) Mixed models involving prezygotic, zygotic, sexual, and fertility selection; (2) Multiple allelic models in which non-monotone covergence occurs for some fitness sets and initial conditions; (3) Cases in which social interaction of pair-wise or higher order influences viability; (4) Mechanisms of molecular turnover which exhibit a formal analogy with meiotic drive models. The proposed research will provide general evolutionary principles for broad classes of models generally acknowledged to be of biological importance, but where present theoretical understanding is very limited. Most significantly, the proposed line of research offers a method for unifying many special cases in population genetics theory.